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Question-122423




Question Number 122423 by ajfour last updated on 16/Nov/20
Commented by ajfour last updated on 16/Nov/20
If  b<a<2b  and θ_(max) =30°  find side s of square.
$${If}\:\:{b}<{a}<\mathrm{2}{b}\:\:{and}\:\theta_{{max}} =\mathrm{30}° \\ $$$${find}\:{side}\:{s}\:{of}\:{square}. \\ $$
Commented by mr W last updated on 17/Nov/20
b tan θ+s cos θ=a  s=((a−b tan θ)/(cos θ))
$${b}\:\mathrm{tan}\:\theta+{s}\:\mathrm{cos}\:\theta={a} \\ $$$${s}=\frac{{a}−{b}\:\mathrm{tan}\:\theta}{\mathrm{cos}\:\theta} \\ $$
Commented by ajfour last updated on 17/Nov/20
thanks sir!  Only if you shall entertain this  additional question, Sir..    If the square plate is released at  this   θ_(max)   at rest, find at what  angle shall it loose contact wirh  the right wall of the fixed  rectangular container?
$${thanks}\:{sir}! \\ $$$${Only}\:{if}\:{you}\:{shall}\:{entertain}\:{this} \\ $$$${additional}\:{question},\:{Sir}.. \\ $$$$ \\ $$$${If}\:{the}\:{square}\:{plate}\:{is}\:{released}\:{at} \\ $$$${this}\:\:\:\theta_{{max}} \:\:{at}\:{rest},\:{find}\:{at}\:{what} \\ $$$${angle}\:{shall}\:{it}\:{loose}\:{contact}\:{wirh} \\ $$$${the}\:{right}\:{wall}\:{of}\:{the}\:{fixed} \\ $$$${rectangular}\:{container}? \\ $$
Commented by mr W last updated on 18/Nov/20
seems unsolvable for me, since we  have three contact forces.
$${seems}\:{unsolvable}\:{for}\:{me},\:{since}\:{we} \\ $$$${have}\:{three}\:{contact}\:{forces}. \\ $$

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